1. Running a lottery over the Internet. There are a lot of people who would be happy to buy a share in a typical national lottery as long as they could be sure they were not getting cheated. I don't care if e.g. 10% of the money goes to fund schools, as long as it's fair and transparent.
2. Internet gambling. If I bet on something, I want the odds to accurately reflect the bets of all the players, and I want to be able to get my money out if I win.
3. A currency for use in online advertising. A lot of the money that advertisers pay mysteriously disappears into the hands of middlemen before it gets to the sites that host the ads. There is also a lot of fraud. Having a transparent and accountable system would make it more effective for people who are not parasites.
Anything else?